Profinite genus of HNN-extensions with finite associated subgroups

We study the profinite genus of HNN-extensions whose associated subgroups are finite. We give precise formulas for the number of isomorphism classes of HNN(G,H,K,t,f) and of its profinite completion and compute the profinite genus of such an HNN-extension HNN(G,H,K,t,f). We also list various situations when HNN(G,H,K,t,f) is determined by its profinite completion.